Dell XPS M1530 boot-up problem (solved?)

I am trying to fix a Dell XPS M1530 that has what appears to be a very common problem for this computer, an all black screen, and no ability to turn on for more than a few seconds. The screen remains black.

There are articles and videos all over the internet about this problem. It was diagnosed and a repair method posted in this forum link:

Having read through the whole discussion, I got to the last response, suggesting we start a new thread for this problem.

Anyway, I have the XPS M1530 problem. Following the suggestions in the old thread, I removed the fan assembly, and cleaned out the dirt and dust. We tried to get the NVIDIA chip to start working by running the computer with the fan assembly held away from the NVIDIA chip (as suggested in the old thread), which got the NVIDIA chip warm, but not really hot. It was good to see that the video started working, and we "almost" got the laptop to boot - but it would always shut down after maybe half a minute or so.

With nothing to lose really, we followed the suggested procedure, using a heat gun set for 600 degrees, and heating the NVIDIA chip for about a minute or so, hopefully long enough to re-melt the solder connections and allow the bad connection to repair itself. Amazingly, it actually seemed to work!

It is now three days later, and the laptop has been running during most of this time. I've cleared out the old data, and little by little, done all the Windows Vista updates, apparently from 2008 through now. The laptop seems to be running just fine, and not getting excessively hot.

My question here, is does anyone know how long this is likely to last? Are we fixing an original proglem, which will continue to work fine once the solder is melted enough to restore all the connections, or is whatever the defect is in the NVIDIA chip something that will happen again - the appropriate word being "when", not "if". If it's still a ticking time bomb, there is no point in using the laptop, as it will completely die again. On the other hand, if heating the NVIDIA chip with a 600 degree heat gun can fix the defect in the chip, then maybe it's safe to start using the laptop, doing periodic backups, as one would do with any computer to be safe.

Follow-up questions, if anyone can advise:
a) Since this is a known defect, can I get DELL to exchange the motherboard for a new one, even though the laptop's warranty has run out?

b) DELL told me they would send a shipping box to me, and I could send the computer back to them where anything/everything would be fixed, for $370. I don't think that includes the battery, which is probably going to need replacement in the not too far off future. The XPS 1530 seems to sell for around $300 now. Even though the guys at Dell tech support tell me how great this laptop was/is, in today's world is it still useful, or just a relic?

c) The laptop has Windows Home Premium on it. Is there any way to get Windows Home Premium to do a full backup (disk image and incremental backup sets) of everything on the hard drive?

d) Is there some way to get Windows Home Premium to create a "boot disk" DVD, so if something gets corrupted, I would have a way to get "into" the system to repair it? As of now, I don't have any DVDs. There is a "recovery partition" on this laptop, but I think one needs to create one or more DVDs ahead of time in order to use the restore functions. ...not sure, never done this yet.